Best bet is a proper back breaker trap (as said above) tethered to something solid just in case.
Rats and mice do not tend to co-habit so evidence of mice (if fresh) could be a sign you don’t have rats. Obviously each has an appropriately sized trap.
You usually do not get just one, and two of either can become a lot of either very quickly.
We had both in our house, mice in loft and rats under floor, and only managed to control it by killing as many of the sods as possible using both traps and multiple types of poison (rat poison slow to kill mice according to the experts – they didn’t charge us any extra btw so not in their interests to mislead, but we ended up with a block that had two types of poison as well as grain bait for mice).